Compression modes and the nuclear matter incompressibility coefficient

We review the current status of the nuclear matter (N = Z and no Coulomb interaction) incompressibility coefficient, K-nm, and describe the theoretical and the experimental methods used to determine K-nm from properties of compression modes in nuclei. In particular we consider the long standing problem of the conflicting results obtained for K-nm, deduced from experimental data on excitation cross sections for the isoscalar giant monopole resonance (ISGMR) and data for the isoscalar giant dipole resonance (ISGDR).